Prog. Theor. Phys. Vol. 46 No. 1 (1971) pp. 308-331
Generalization of Quantum Field Theory on the Basis of Function Manifold
Department of Physics, Fukusima University, Fukusima
(Received December 13, 1968)
A function manifold can be regarded as a unity of space-time and matter. Based on this circumstance an attempt is made to generalize the local quantum field theory to quantum field theory on a function manifold. A Lagrangian theory for the interacting Dirac and vector gauge fields is studied as a definite model theory. A c-number field on the manifold is equivalent to a composite of certain basic quanta, so that we come to deal with these composite systems in place of space-time functions in the local theory.
It is shown that our interaction has a non-local feature. Furthermore, in place of an algebraic self-consistent mass equation for elementary particles of a local field theory, we have a self-consistent integral mass eigenvalue equation for the composite fields representing an elementary particle. Owing to these properties it is shown that perhaps the difficulty of the ultraviolet divergence will principally be overcome.
DOI : 10.1143/PTP.46.308
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